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\begin{center}  ���ѧϰ�ľ����ʽ�Ƶ�������matconvNet��ܣ�   \end{center}
$$\frac{\partial p_i}{\partial z_i}=p_i-p_i^2, \frac{\partial p_j}{\partial z_i}=-p_ip_j$$
\begin{equation*}
\begin{aligned}
\frac{\partial l}{\partial z_i}
&=\sum_{j=1}^N\frac{\partial l}{\partial p_j}\frac{\partial p_j}{\partial z_i}\\
&=\sum_{j=1}^N d_j\frac{\partial p_j}{\partial z_i}\\
&=d_i(p_i(-p_1-p_2\ldots -p_N+1))
\end{aligned}
\end{equation*}


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